Theorem e3bir

Description: Right biconditional form of e3 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e3bir.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
	e3bir.2	⊢ ( 𝜏 ↔ 𝜃 )
Assertion	e3bir	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e3bir.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2		e3bir.2	⊢ ( 𝜏 ↔ 𝜃 )
3	2	biimpri	⊢ ( 𝜃 → 𝜏 )
4	1 3	e3	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )